What is expand (e^x-1)(e^x-x)^2 ?

The solution to expand (e^x-1)(e^x-x)^2 is e^{3x}-2e^{2x}x+e^xx^2-e^{2x}+2e^xx-x^2

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expand (e^x-1)(e^x-x)^2

expand

(e^{x} - 1) (e^{x} - x)^{2}

e^{3 x} - 2 e^{2 x} x + e^{x} x^{2} - e^{2 x} + 2 e^{x} x - x^{2}

Solution steps

(e^{x} - 1) (e^{x} - x)^{2}

Apply the distributive law:

a (b - c) = ab - a c

a = (e^{x} - x)^{2}, b = e^{x}, c = 1

= (e^{x} - x)^{2} e^{x} - (e^{x} - x)^{2} \cdot 1

= e^{x} (e^{x} - x)^{2} - 1 \cdot (e^{x} - x)^{2}

Simplify

e^{x} (e^{x} - x)^{2} - 1 \cdot (e^{x} - x)^{2} : e^{3 x} - 2 e^{2 x} x + e^{x} x^{2} - e^{2 x} + 2 e^{x} x - x^{2}

= e^{3 x} - 2 e^{2 x} x + e^{x} x^{2} - e^{2 x} + 2 e^{x} x - x^{2}

(2 x^{2} + 3 x - 3) e^{x}

\frac{( x + 2 ) \cdot ( x + 1 )}{2 x}

\frac{k - 5}{k ( 5 k + 1 )}

\frac{1}{( ( s ^{2} + 2 s + 1 ) ( s + 1 ) )}

(1 + x + x^{2})^{9}

What is expand (e^x-1)(e^x-x)^2 ?
The solution to expand (e^x-1)(e^x-x)^2 is e^{3x}-2e^{2x}x+e^xx^2-e^{2x}+2e^xx-x^2